A common link between the IQHE and the Riemann zeros perhaps comes from random matrix theory, since the latter has been applied to both the Riemann zeros and to disordered systems. This is an appealing connection, to be contrasted to the hamiltonians proposed toward a realization of
the Hilbert-Pólya idea. Proposals such as \(H= xp\)  and variations are not random hamiltonians; instead the randomness of the zeros is attributed to the chaotic behavior of such hamiltonians [1]}, which is very different than a particle moving in a random landscape, such as in the IQHE.
In fact, relatively recently, random matrix theory was applied to a study of the extreme values of the zeta function on the critical line
by making an analogy with the so-called freezing transition in disordered landscapes [2]}, [3]},
and such a freezing transition is expected to play a role in the IQHE in order to understand its multi-fractal properties.
